In previous railroad grade crossing protection systems, it was conventional practice to sense the motion of an approaching train by continuously monitoring the track impedance and by detecting the change in the impedance to attempt to provide a constant warning time. It will be appreciated that the reliability of the motion sensing and the accuracy of the time-of-arrival prediction are dependent upon the linear relationship between the track impedance and the distance to an oncoming train. However, under certain conditions, the distance that a train is from the highway crossing is not always directly proportional to the impedance which appears across the track rails. In a majority of existing continuous motion detection systems, an analog computation process is then performed to detect motion. Thus, the reflected track impedance signal is then differentiated, and the change in the impedance corresponds to the purported velocity of the approaching train. In some of the prior art motion detectors, only the velocity signal is utilized to determine movement. However, in more sophisticated motion detection systems, the distance and velocity signals are combined in an endeavor to predict train arrival and to provide a constant warning time. It has been found that these prior motion detectors were possessed of several shortcomings. For example, in coded cab signal territory, interference and inaccuracy occur due to the intermittent change in the track impedance which is presented to the motion sensor. That is, the motion detector is susceptible to interference from coded track circuits due to the alternate loading and unloading of the track by the code transmitter. Thus, it will be appreciated that continuous analog computation which is presently employed in existing motion monitors is difficult to accurately achieve even under constant velocity conditions. Even in more sophisticated constant warning predictors, the time of arrival of the train at the crossing is only possible when the oncoming train is moving at a constant velocity. However, there is a long felt need of sensing the motion and of providing a constant warning time in crossing areas where the trains accelerate, decelerate, or even stop in the approach zones. While there have been previous attempts to satisfactorily accomplish such operation with existing techniques, the end result was found to be extremely complex and prohibitively expensive. Thus, there is a genuine exigency to develop a viable motion detector and time-of-arrival predictor which provides a constant warning time in crossing areas where trains accelerate, decelerate, stop, and start in the approach zones.